Sesame Workshop, the nonprofit group behind the children’s television program, has struck a five-year deal with HBO, the premium cable network, that will bring first-run episodes of “Sesame Street” exclusively to HBO and its streaming outlets starting in the fall.

The partnership, announced Thursday, will allow the financially challenged Sesame Workshop to significantly increase its production of “Sesame Street” episodes and other new programming. The group will produce 35 new “Sesame Street” episodes a year, up from the 18 it now produces. It will also create a spinoff series based on the “Sesame Street” Muppets along with another new educational series for children.

After nine months of appearing only on HBO, the shows will be available free on PBS, home to “Sesame Street” for the last 45 years.

It is an unexpected union: the nonprofit behind a TV show created to teach children in underserved communities matched with the premium cable network that targets affluent adults with innovative programming. But the deal speaks to the digital transformation upending the television business, primarily the explosion of streaming video creating a generation of children who watch shows on demand, often on a mobile phone or tablet, instead of flipping on a TV.

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Big Bird with Tina Fey as Mother Goose and Alan Muraoka on “Sesame Street.” The partnership with HBO will allow Sesame Workshop to significantly increase its production of “Sesame Street” episodes. Credit Richard Termine/Sesame Street For Sesame Workshop, the deal helps alleviate funding pressures the group has faced, especially since important revenues from sources like DVD sales have eroded. HBO, in turn, becomes a stronger force in children’s TV, a valuable area of programming as it pushes further into streaming and seeks subscriber growth.

Still, Sesame Street’s decision to broadcast its new shows on a premium pay-TV service like HBO — and not free on PBS until months later — drew an immediate backlash. On social media, hundreds of commentators said that the arrangement with HBO created a perception of an economic class divide, with PBS favoring privileged children and jettisoning its commitment to less-advantaged ones, whom the show was originally aimed at.

“Kids are getting squeezed in the middle,” said Tim Winter, president of the Parents Television Council, a nonpartisan education group that advocates for responsible entertainment. “In order to watch original episodes of the most iconic children’s program in television history, parents are now forced to fork over about $180 per year and subscribe to the most sexually explicit, most graphically violent television network in America. I can’t imagine a greater juxtaposition in television than this.”

The group called for HBO to allow nonsubscribers to watch original “Sesame Street” episodes free.

In a statement, an HBO spokesman said, “We are incredibly proud of our role in securing the future of ‘Sesame Street’ and its availability to PBS for free.”

Other critics said that the Sesame-HBO partnership could undermine its pedagogical mission.

Dr. Michael Rich, director of the Center on Media and Child Health in Boston, said he feared that Sesame Workshop will face either overt or implicit pressure to create new programming or spinoffs that are more commercial and less educational. Dr. Rich also said the deal could starve PBS of its public funding, with one of its flagship properties now available on HBO.

“I am worried about the future of PBS,” he said. “Not only is ‘Sesame Street’ currently a flagship property, but it may start a trend with other programming.”

PBS, Sesame Workshop and HBO defended the partnership as a critical development necessary to continue to produce “Sesame Street” and to further Sesame’s objectives.

HBO already offers some children’s programming.

“No other media company believes that disadvantaged kids deserve the same shot as middle-class kids, and that remains important to us,” said Jeffrey D. Dunn, chief executive of Sesame Workshop. “We will have a couple of homes now. HBO will allow us to really capture the consumer shift, but we are not leaving linear TV.”

Indeed, “Sesame Street” will continue its run uninterrupted on PBS this fall, with the season featuring a selection of episodes from the last few seasons edited in new ways. Mr. Dunn emphasized that “Sesame Street” typically featured a mix of new and old episodes each season, and its preschool audience likes to watch episodes over and over, which increases their educational impact.

“Timing does not matter to kids,” he said. “The more they watch it, the more they like it.”

Episodes will also continue to be available for streaming on PBSKids.org and the PBS Kids video app, which offer four episodes at a time and are refreshed each week. About two-thirds of children now first discover “Sesame Street” on demand, Mr. Dunn said.

“Sesame Workshop’s new partnership does not change the fundamental role PBS and stations play in the lives of families,” Anne Bentley, a PBS spokeswoman, said in a statement.

Sesame Workshop’s partnership with HBO is expected to shore up its finances. The group’s revenue sources include product licensing on Sesame-branded merchandise, as well as support from corporations, government agencies and foundations.

Historically, less than 10 percent of its funding for “Sesame Street” episodes have come from PBS, with the largest source of income from videocassette or DVD sales. But with the rapid rise of streaming and on-demand viewing, DVD sales have plummeted, buffeting Sesame’s business.

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The singer Janelle MonŠe serenaded Cookie Monster with “The Power of Yet” in a 2014 appearance on “Sesame Street.” Credit Richard Termine/Sesame Workshop PBS was not able to increase its payments to Sesame, forcing it to cut back on the number of episodes it produced and the creation of other new material. Now, PBS will not pay Sesame Workshop a licensing fee, which now is about $4 million a year, according to an executive with knowledge of the funding who spoke on the condition of anonymity.

In 2014, Sesame Workshop lost $11 million, according to its audited financial statement. Its total operating revenues were $104 million, down nearly 14 percent from the previous year.

It is not clear how much HBO is paying, as financial terms of the deal were not disclosed.

“In order to fund our nonprofit mission with a sustainable business model, Sesame Workshop must recognize these changes and adapt to the times,” said Joan Ganz Cooney, who co-created “Sesame Street” in the late 1960s.

For HBO, the partnership provides the network with prestigious and popular television programming for both its cable network and its new stand-alone streaming service HBO Now, which is aimed at people who do not have or do not want cable TV subscriptions.

In addition to the new series, HBO licensed more than 150 library episodes of “Sesame Street.” It also licensed about 50 past episodes of “Pinky Dinky Doo” and “The Electric Company” from Sesame Workshop.

“ ‘Sesame Street’ stands for excellence and quality in children’s programming, and we stand for excellence and quality in all programming,” said Richard Plepler, chief executive of HBO.

Currently, there is a race among streaming services for children’s programming, with the outlets recognizing that they can entice parents to subscribe if they capture their children’s attention. Amazon, Netflix and other online outlets are pouring resources into acquiring and developing their own original children’s series.

Mr. Dunn said that Sesame had talked to a number of HBO’s competitors before settling on a deal. As a result of the HBO partnership, “Sesame Street” episodes will no longer be available on Amazon and Netflix.

This is not the first time that Sesame and HBO crossed paths, with “Sesame Street” creating parodies of a number of popular HBO series over the years. On Thursday, people used Twitter to brainstorm about how the two brands could work together even more closely. One suggestion was to cast Bert and Ernie as the stars of the next season of “True Detective,” HBO’s dark crime drama.

Correction: August 13, 2015
An earlier version of this article misstated Sesame Workshop’s deal partner in one instance. As the article states elsewhere, it is HBO, not PBS.